J. Phys. Chem. 1994, 98, 12635-12640
12635
Rates of Alkyl Radical-Radical, Alkyl Radical-Iodine, and Iodine Atom- Atom Reactions in Normal Alkanes and Cycloalkanes Jay A. Laverne* and Laszlo Wojnarovitst Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556 Received: August 8, 1994; In Final Form: September 28, 1994@
Pulse radiolysis techniques have been used to determine the second order rate constants for radical-radical O normal alkanes of reactions of the parent alkyl radicals produced in neat liquid cycloalkanes of CS to C ~ and c 6 to C17. Iodine solutions of these compounds were used to determine the radical scavenging rate constants, the extinction coefficients of the iodine atom produced from this reaction, and the second-order rate constants for the subsequent reactions of the iodine atoms. None of the three sets of rate constants were found to be completely proportional to the inverse of the viscosity of the media, indicating that they are not solely diffusion rate-controlled. However, it was possible to describe the observed rate constants for the alkyl radicaliodine and iodine atom-atom reactions with a combination of a diffusion-controlled rate constant which scales inversely with the viscosity of the media and an activation-controlled rate constant which is the same for all media. The same procedure also worked for the alkyl radical-radical reactions except that the diffusioncontrolled rate constant was further modified by a spin-steric factor. No significant differences were observed in all three sets of rate constants for the normal alkanes or the cycloalkanes at the same viscosity.
Introduction
tion also produces an iodine atom which was suggested to form a charge transfer complex in cyclohexane before eventually The radiolysis of normal alkanes and cycloalkanes makes up recombining to produce molecular iodine.6 Although there have a large fraction of all radiation chemical studies.' Although been numerous studies of the photolytically produced iodine each hydrocarbon undergoes slightly different chemistry, one atom geminate recombination in hydrocarbons,20pulse radiolytic of the major uncharged reactive species produced by the passage studies of the kinetics of the iodine atom have only been of ionizing radiation is the parent alkyl radical. In cycloalkanes performed in cyclohexane.6 Competition between radicalthis is a single radical while in the normal alkanes a number of radical reaction and radical scavenging by iodine is a very different radicals are possible, but the secondary ones dominate important method of determining the initial radical concentrathe yield., Since the major portion of the yields of the stable tions for different types of radiations. Information on iodine end products are formed by disproportionation and combination scavenging reactions in a number of different hydrocarbons reactions of these radicals, it is very important to know the would be helpful for these types of studies. appropriate rate constants. The rate constants for ~yclopentyl,~-~ Fast electron pulse radiolysis studies of CSto Clo cycloalkanes c y ~ l o h e x y l , ~ ~n ~- h- 'e~~ y l , ~and , ' ~ n-dodecyl radicals15 are the (26 to C17 normal alkanes were performed. These studies and only ones which have been measured, and there is a considerable used optical absorption techniques to directly observe the decay amount of discrepancy between some of the determinations. of the alkyl radicals produced in the pulse. Measurements of Clearly, accurate rate constants for the alkyl radicals produced the formation and the decay of the iodine atoms produced in in their parent medium are necessary for the proper understandthe radiolysis of iodine solutions of these hydrocarbons were ing and modeling of the radiation chemistry of hydrocarbons. used to determine the radical scavenging rate constant, the Some of the earliest radiation chemical studies used iodine extinction coefficient of the iodine atom, and the rate constant to elucidate the reaction mechanism in hydrocarbon radiolyfor its combination reaction. sis. 16,17 The competing chemical reactions involved in these systems are given in the following scheme. Experimental Section R'
+ R' -products k0
R' + I,
kl
RI
+ I'
(RO) (R1)
Iodine is a very efficient radical scavenger, and the yield of the alkyl iodide formed can readily be measured using a number of analytical techniques. Unfortunately, the radical scavenging rate constants of iodine have only been determined in cycloc y ~ l o h e x a n e ,and ~ . ~n-he~adecane.'~ ~~~~ This react Permanent address: Institute of Isotopes of the Hungarian Academy of Sciences, P.O. Box 77, Budapest, H-1525, Hungary. Abstract published in Advance ACS Abstracts, November 1, 1994. @
0022-365419412098-12635$04.50/0
The pulse radiolysis experiments were performed with the Radiation Laboratory LINAC facility using nominal 50 ns wide pulses of 9 MeV electrons. The accelerator, optical detection equipment, and signal-averaging techniques are described elsewhere.21~22The radiolysis cell was made from a square Supracil tube with an optical path length of 1 cm. The solutions were degassed with ultrahigh-purity nitrogen which flowed through the cell continuously throughout the experiment. A prebubbler was used for the iodine solutions of the more volatile hydrocarbons. Dosimetry was performed with NzO-saturated M SCN- solutions using the following parameters for the observed (SCN),-: A = 472 nm, E = 7580 M-' cm-', G = 6.14 molecules/100 eV. Corrections were made for the differences between the electron densities of the hydrocarbons and water. The dose levels per pulse normally were held to within 10% at 400 rad for the iodine scavenging experiments and 900 0 1994 American Chemical Society
Laverne and Wojnarovits
12636 J, Phys. Chem., Vol. 98, No. 48, 1994
U
0 -1
'0'
2
1
3
4
5
Time (psec) Figure 1. Time dependence of the relative absorption of cyclooctyl radicals in neat cyclooctane (open symbols) at a dose of about 700 rad and of iodine atoms (closed symbols) in 0.5 mM iodine solutions of cyclooctane at doses of about 200, 400, and 700 rad.
rad for the neat solutions. In some so-noted experiments the dose was varied from 200 to 900 rad. The formation and decay of the iodine atom were monitored at 330 nm in all hydrocarbons, and 50- 100 pulses were averaged. Iodine concentrations were varied from 0.1 to 1 mM with most irradiations at 0.5 mM or less. The decay of the alkyl radicals was followed at 260 nm. All of the measurements were made at 25 "C. The hydrocarbons were purified of all unsaturated compounds by passing them through a 70 cm long column (i.d. 2 cm) containing silver nitrate on alumina prepared by the method of Murray and Keller.23 Gas chromatographic-mass spectrometric analysis of the cycloalkanes showed no detectable unsaturated impurities.
Results and Discussion Alkyl Radical-Radical Reactions in Neat Hydrocarbons. The alkyl radicals are produced at times short compared to the electron beam pulse by ion-molecule reactions which also give H2 and by decomposition reactions of excited molecules which also give H atoms.' With fast electron radiolysis H atoms will mainly undergo abstraction reactions with the medium to form more alkyl radicals. Very few measurements of the rate constant for this reaction in hydrocarbons have been made, but it is expected to be in the range of lo7 M-' s - ' . * ~ Other fast pulse
radiolysis experiments have shown that the formation of alkyl radicals is complete on the picosecond time scale.25 For the purposes of this study it can therefore be assumed that all of the alkyl radicals are formed instantaneously compared to their time period of reaction. Figure 1 shows the formation of the cyclooctyl radical observed at 260 nm in cyclooctane at a dose of about 700 rad. If the G value26of the cyclooctyl radical is taken to be 5 radicals/100 eV,27then its concentration is about 3 pM and reasonably constant for several microseconds. The plateau region of the optical absorption curves like that shown in Figure 1 for cyclooctane was measured for each of the hydrocarbons. The so-obtained optical densities were used in conjunction with the corresponding signal of the thiocyanate dosimeter to determine the product of the G value and the optical extinction coefficient, E , for each of the alkyl radicals. Table 1 gives the values of G E (radicals/(100 eV M cm)) obtained in this manner. For some unknown reason there is a large variation in the values of GEfor the cycloalkaneswhile the normal alkanes seem to show a slight increase in the value of GEwith increasing carbon number. Absorption spectra were taken for a few alkyl radicals formed in the cycloalkanes; the peaks of the absorption curves for the lighter hydrocarbons are 1250 nm, and they shift slightly to the red with increasing carbon number. This shift into the region of 260 nm where the values of GEwere measured may account for some of the observed increase. However, the absorption spectra were generally very flat, and a shift of the spectra cannot completely account for the large variations in G Eobserved for the cycloalkanes. Accurate values of the alkyl radical yields are not known for all of the hydrocarbons. In many cases the yields simply have not been measured, and in other cases the values are very suspect because of the scavenging technique or the high radiation dose used. Recent iodine scavenging experiments on some of the cycloalkanes with very low (25 krad) doses have found yields of 4.1, 4.9, and 4.6 radicals/100 eV for cyclopentyl,28cycloand c y c l ~ o c t y lradicals, ~~ respectively. The use of tritium iodide as a radical scavenger in normal alkanes30 found parent alkyl radical yields of 4.75 in n-hexane, 4.91 in n-octane, 5.2 in n-nonane, 5.00 in n-decane, 5.33 in n-dodecane, 5.41 in n-tetradecane,and 5.53 in n-hexadecane. For simplicity, a value of 5.0 radicals/100 eV has been assumed for all alkyl radical yields. Except for cyclopentyl radicals, this value is within 10% of the measured values, and such an assumption should have little consequences on subsequent conclusions in this work. The extinction coefficients are then found to range from about 400
TABLE 1: Reaction of Alkvl Radicals Produced in the Hydrocarbons density, g/cm3 GE" 2k&& x 2k& x M-I s-I D(R) x lo9, m2 s-l ~~~
C-CSHIO C-C~HIZ c-C~HI~ C-CsH16 c-CloH20
0.746 0.779 0.810 0.835 0.871
1679 3510 2686 3737 2835
7.49 2.88 2.75 1.15 0.88
2.52 2.02 1.48 0.86 0.50
0.660 0.684 0.703 0.718 0.730 0.740 0.749 0.756 0.763 0.769 0.773 0.778
1895 1955 2248 2497 2645 2286 2596 2362 2403 2750 3003 2690
10.1 7.46 5.12 4.91 3.57 3.53 3.09 2.53 2.38 2.14 1.29 1.17
3.83 2.92 2.30 2.45 1.89 1.61 1.60 1.20 1.14 1.18 0.77 0.63
q, mPa s effective reaction distance, W?,nm
3.23d 1.39d 0.87d 0.57d 0.33d
0.423d 0.905d 1.331d 2.263d 4.047d
0.13 0.14 0.16 0.14 0.14
4.21' 3.12' 2.00' 1.70' 1.31' 1.OY 0.82f 0.67f
0.29' 0.38' 0.51' 0.67' 0.85' 1.088 1.378 1.709 2.009 2.868 3.099 4.038
0.15 0.15 0.18 0.16 0.16 0.16 0.16 0.16 0.16 0.14 0.15 0.14
0.5u 0.W 0.3g 0.32f
kobs in units of M-I s-l, a G in units of radicals/100 eV, E in units of M-I cm-I. Reference 33. e Reference 34. f Reference 35. 8 Reference 36.
E
in units of M-l cm-I. Assume G = 5 radicalsll00 eV.
J. Phys. Chem., Vol. 98, No. 48, 1994 12637
Rates of Radical Reactions in Alkanes to 800 M-l cm-'. There is an extremely wide variation of values for radical extinction coefficients in the literature mainly because they are so small and difficult to measure and also because of the various assumptions used to convert from the actual quantities that are measured. The alkyl radical decays were observed to be complete on time scales that increased from about 0.1 to several milliseconds with increasing carbon number. Plots of the inverse of the optical densities as a function of time were found to be very linear in the initial decay region for at least two half-lives. They were also found to be independent of dose. A least-squares fitting of the initial decays was used to obtain the slopes which are proportional to the observed second-orderrate constant, 2&bs, divided by the extinction coefficient, E. The optical absorptions observed with these hydrocarbons are low and inherently more uncertain than in most other pulse radiolysis experiments. However, the quantities 2ko& and E have inverse dependences on the optical absorption, and there is somewhat of a compensation effect on the value for the observed rate constant, 2k0bs.31 The observed rate constants for the alkyl radical-radical reactions are given in Table 1. With increasing carbon number the value of 2k0b, decreases by about a factor of 5 for the cycloalkanes and 6 for the normal alkanes. Most of the values of 2k0bsin Table 1 agree very well with those available in the literature for the alkyl radical in the parent medium. Extrapolation of the measured value of Smaller et aL3 to room temperature gives 2.8 x lo9 M-' s-l for cyclopentyl radicals in cyclopentane. Rate constants for the reaction of cyclohexyl radicals in c y ~ l o h e x a n e ~range ~ ~ - ~from ~ 1.2 x lo9 to 4 x lo9 M-' s-' with most of the recent measurements at about 2.4 x lo9 M-' s-l. The present results are somewhat lower than those of Sauer and Manis for n-hexane (6.2 x lo9 M-' s-l) and of Ladygin et al.15 for n-dodecane (2.4 x lo9 M-' s-l). The rate constant for a diffusion-limitedreaction of uncharged species in the long time limit was developed by Smoluch~wski.~~ This relationship is given by
where N is Avogadro's number, DAB(m2 s-') is the sum of the diffusion coefficients of the two reactants, and the effective reaction distance, RAB(m), is the sum of the effective reactant radii. The dependence of the diffusion coefficient for an uncharged species on the viscosity of the medium, q, can sometimes be represented by the Stokes-Einstein relationship, DA = kbT/(6nqR~),where kb is Boltzmann's constant, T i s the temperature in Kelvin, and RAis the effective diffusion radius. For the reaction of two different species eq 1 can then be transformed to
by substituting the Stokes-Einstein relationship for the diffusion coefficient of each reactant. For the reaction of two like species, RA is set equal to RB and kd is replaced by 2kd to avoid counting each reaction twice. Furthermore, it is normal to set the effective reacdon distance equal to the sum of the effective diffusion radii. Equation 2 for like species is then transformed to the following:
The forms of eqs 1 and 3 suggest that to a first approximation the rate constants for alkyl radical-radical reactions should be proportional to the self-diffusion coefficients or to the inverse of the viscosity of the media. Values of the self-diffusion
6 5
"
0
1
2
3
4
l/viscosity (mpa-' 5.') Figure 2. Dependence of the self-diffusion coefficients as a function of the inverse viscosity. The circles are for the cycloalkanes, and the squares are for the normal alkanes. The diffusion coefficients for iodine molecules in several alkanes are given by the diamonds.
3 h
r
v) r
%2
?
0 7
X
Y 1
cu
0
I
I
I
1
2
3
4
1/viscosity (rnpa-' s-') Figure 3. Rate constants of alkyl radical-radical reactions as a function of the inverse viscosity. The circles are for the cycloalkanes, and the squares are for the normal alkanes. The dashed line is the predicted diffusion-controlled rate constant from eq 3, and the solid line is from eq 4 with k, = 5.26 x lo9M-' s-' and @kd = 2.73 x 109/qM-' mPa.
coefficients and the viscosities of the hydrocarbons are given in Table 1.33-36 As seen in Figure 2, the self-diffusion coefficients appear to be linearly dependent on the inverse of the viscosity. Such a dependence is expected from the StokesEinstein relationship if R, is nearly constant for the molecules studied.37 Substituting the constants into eq 3 gives the diffusioncontrolled rate constant as 6.6 x 109/q M-' s-l where the viscosity, q, is given in the standard unit of mPa s (1 mPa s = 1 cP). Applying this relationship to water ( q = 0.89) gives a value of 7.4 x lo9 M-' s-l for the rate constant of a diffusioncontrolled reaction. This value is 2-4 times lower than the fastest reactions measured for uncharged species in water.38 Many photochemical reactions in hydrocarbons, e.g., quenching of excited singlet states, are diffusion-controlled, and the measured rate constants39are similarly greater than predicted by eqs 2 and 3. Therefore, the collision frequencies corresponding to the diffusion-controlledrates of eqs 2 or 3 are lower limits. The apparent discrepancy is probably due to the assumptions used to derive the equations and setting the reaction diameter equal to the sum of the diffusion radii. The observed rate constants for the alkyl radical-radical reactions are shown in Figure 3 as a function of the inverse viscosity. At the same viscosity there does not appear to be
12638 J. Phys. Chem., Vol. 98, No. 48, 1994
Laverne and Wojnarovits
any difference between the rate constants for the normal alkanes and the cycloalkanes. It is clear that for most of the hydrocarbons studied here the rate constants are not proportional to the inverse of viscosity. Only at very high viscosities do the rate constants seem to scale with the inverse viscosity in a manner consistent with eq 3. It should be noted that over a limited range of viscosities some of the rate constants in Figure 3 may lie on a straight line, but such a line would not pass through the origin as it should in a true diffusion rate-controlledreaction. The dashed line in Figure 3 shows that in all cases the predicted lower limit for a diffusion-controlled rate constant is much greater than the observed rate constant. The diffusion-controlled reaction rate constants given by eqs 1-3 determine only the frequency of encounters between reacting species. The actual observed rate constant will be slower than diffusion controlled if any process prevents every encounter from leading to product formation or an activated complex which has a relatively long lifetime is formed. The observed rate constant, kobs, can then be described by the following combination of a diffusion-controlled rate constant, Qkd, and an activation-controlled rate constant, k,.32
kobs= @k,k,/(Qk,
+ k,)
(4)
Here the classical paper by Schuh and FischefiO has been followed in which diffusion-controlled rate constant has been modified by a parameter Q to give the fraction of encounters that lead to formation of an activated complex. The value of Q is given by the product of the steric factor, Dst,and the spin factor, Qsp. For the alkyl radicals the spin factor will be l/4 if the three triplet states cannot lead to product formation. However, during the collision process the radicals may be in close proximity for a considerable period of time, especially for the high-viscosity media, so that spin relaxation may occur with the result that Q, = 1. A simple calculation shows that the spin relaxation will occur on the time scale of about 3 ns, and for even the highest-viscosity hydrocarbons studied here this is sufficient time for the radicals to diffuse several nanometers apart. Spin relaxation is therefore not expected to occur, and for the reaction of alkyl radicals QSp = l/4. It is normally assumed that there is no steric hindrance for small radicals and QSt = 1, but the hydrocarbons studied here are physically large and Qstmay be much less than one. The observed rate constants for alkyl radical-radical reactions were fit using least-squares techniques to an equation like (4) where k, was assumed to be constant and Qkd was assumed to be inversely proportional to the viscosity. The resulting parameters are k, = 5.26 x lo9 M-' s-l and Qkd = 2.73 x 109/r M-'mPa, and a calculated curve is shown in Figure 3. The value for Qkd is about 2.5 times smaller than the diffusioncontrolled rate constant predicted by eq 3, and it is about an order of magnitude slower than measured fast quenching reactions in hydrocarbon^.^^ The magnitude of @kd suggests that in addition to a spin effect there is at least some steric hindrance also. The effective reaction distances for alkyl radical-radical reactions can be estimated by substituting the values for Qk;l into eq 1, and the results are given in Table 1. Actually, the effective reaction distances calculated in this manner are the products of D and the reaction distance. For all of the hydrocarbons studied here the reaction distance is reasonably constant in the range of about 0.13-0.16 nm. It is obvious that the physical sizes of the radicals produced here vary by a large amount; however, the specific reactive sites may be the same for all radicals. If the value of is taken to be about
TABLE 2: Reactions of Alkyl Radicals with Iodine D(I2) x lo9, m2 s-l
effective reation distance, @R, nm
1.49 1.21 0.68 0.57 0.30
3.21 1.77 1.33 0.91 0.61
0.76 0.72 0.70 0.62 0.54
1.68 1.47 1.33 1.26 1.08 0.82 0.66 0.70
4.36 3.50 2.76 2.23 1.86 1.55 1.30 1.11 0.99 0.77 0.73 0.61
0.83 0.82 0.85 0.78 0.76 0.74 0.71 0.68 0.66 0.60 0.60 0.55
k&s x
M-I
s-l
0.55 0.50 0.39 0.39
0.25 because of spin effects, then the true effective reaction distance is close to 0.6 nm or about two carbon-carbon bond lengths. Alkyl Radical-Iodine Scavenging Reactions. Ebert and co-workers performed a thorough study of the reactions of iodine in cyclohexane.6 They observed that the scavenging of the alkyl radicals could be followed by optically observing the iodine atom. They further proposed that the iodine atom forms a charge transfer complex with the bulk medium. Iodine atom or its complex has an absorption maximum at about 330 nm in all the hydrocarbons studied. Reaction R1 may not involve simple kinetics if the formation of the alkyl radical by H atom abstraction is slow. However, as discussed above, such reactions are fast and should be complete within a few nanoseconds. Competition between radical scavenging by iodine and radical formation by H atom abstraction should be negligible if low concentrations of iodine are used. Figure 1 shows the time dependence for the absorption of the iodine atom produced in 0.5 mM iodine solutions of cyclooctane at doses of 200-700 rad. It is observed that the alkyl radical production is complete well before iodine atoms are observed. Observation of the formation of the iodine atoms may also be complicated by the recombination of these atoms to form molecular iodine. At very high doses iodine atom concentrations will be large, and reaction R2 can interfere with the observation of the formation rate of the iodine atom in reaction R1. However, no significant effects were observed at the doses of 400 rad used in the present studies. Figure 1 shows the formation of the iodine atoms in cyclooctane with doses up to about 700 rad and no significant decay of the signal due to reaction R2 is observed on these time scales. However, for some experiments at very low iodine concentrations (0.1 mM) the maximum absorbance was found to be dependent on iodine concentration and is presumably due to the competition between alkyl radical-radical and alkyl radical-iodine reactions. The pseudo-first-order rate constant for reaction R1 can be obtained from the slope of a plot of ln(Am/(Am- A)) as a function of time where A, is the absorbance maximum and A is the time-dependent absorbance. The values of A, were obtained by the time averaging of curves like those in Figure 1. Iodine concentration was varied in some selected experiments in order to confirm that competing reactions had a negligible effect on the absorbance maximum and the kinetics. The rate constants for reaction R1 in the various hydrocarbons are given in Table 2. The agreement of the present results with those of Foldiak and Schuler for cyclopentane (1.9 x 1Olo M-'s-l),I8
J. Phys. Chem., Vol. 98, No. 48, 1994 12639
Rates of Radical Reactions in Alkanes
TABLE 3: Formation and Reaction of Iodine Atoms in Hydrocarbons
GEa
C-C~HIO8367 c-C~HIZ 8448 c - C ~ H I 10567 ~ 8528 C-CIOHZO9100
Figure 4. Rate constants of alkyl radical-iodine scavenging reactions as a function of the inverse viscosity. The circles are for the cycloalkanes, and the squares are for the normal alkanes. The dashed line is the predicted diffusion-controlled rate constant from eq 3, and the solid line is from eq 4 with k, = 2.44 x 1OloM-' s-l and (Pkd = 1.56 x 1O1O/7M-I mPa. cyclohexane (1.2 x 1Olo M-l s-'),18 and n-hexadecane (4.8x lo9 M-' s-l)19 is good. A plot of the rate constants for the alkyl radical-iodine scavenging reactions as a function of inverse viscosity is shown in Figure 4. The dependence of the results on viscosity is almost identical to that obsefved for alkyl radical-radical reactions. At the same viscosity there does not seem to be any major differences between the normal alkanes and the cycloalkanes. A least-squares fitting of the data to eq 4 gave the parameters k, = 2.44 X 10" M-' s-' and (Pkd = 1.56 X lo'o/V M-' mPa. The value for @ k d is much greater than the predicted diffusioncontrolled rate constant using eq 2 (assuming R A B /= ~ RA = RB),which is shown as a dashed line in Figure 4. In fact, @ k d is very nearly equivalent to the rate constants for diffusioncontrolled reactions in water38or the quenching of excited singlet states in hydrocarbon^,^^ suggesting that Q, is very nearly equal to one. Certainly, there are no spin effects in the scavenging of alkyl radicals by iodine, and steric effects can be expected to be small. The effective reaction distance of the alkyl radical-iodine scavenging reactions can be obtained from the above-fitted parameter for @kd if the diffusion coefficients of iodine molecules in the hydrocarbons are known. However, in only a few alkanes have these coefficients been and the values are plotted in Figure 2. It can be seen that the iodine diffusion coefficients do not scale as the inverse of viscosity like the self-diffusion coefficients of the alkanes. Extrapolation to obtain the diffusion coefficients for iodine molecules in the other alkanes must be performed with a different type of scaling. The empirical relationship
D A B ~ /=TA
+ byX
where A , b, and x are fitted parameters has been shown to very accurately predict diffusion coefficient^.^^ Using the literature values for the iodine diffusion coefficients, it was observed that eq 5 does not predict temperature dependences well, but at a given temperature it is found to give excellent results for the different alkanes with x = 0.5. A plot of the diffusion coefficients of iodine as a function of is found to give a good straight line with the parameters A = 2.76 x Pa m2 K-' and b = 8.73 x Pa'" s1I2 m2 K. Values for all the diffusion coefficients for molecular iodine and the calculated
7224 7321 8434 8103 8826 8995 8960 8863 9149 8507 9250 8721
n-C6H14 n-C7H16 n-CsHls n-C9Hzo n-CloH22 n-C11Hx n-CIZH26 n-Ci3Hzs n-C14H3o n-CisH32 n'C16H34 n-C17H36
2kobs X 2ko& x D(1) x lo9, effective reaction 10-7b M-I s-l mz s-l distance, (PR,nm 1.60 2.68 6.42 0.49 1.06 1.79 3.54 0.42 0.70 1.47 2.66 0.38 0.44 0.75 1.82 0.32 0.39 0.71 1.22 0.27 3.80 8.72 2.63 0.53 3.05 7.00 0.50 2.08 1.52 2.56 5.52 0.47 1.48 2.40 4.46 0.45 1.06 1.87 3.72 0.42 0.95 1.71 3.10 0.40 0.52 0.93 2.60 0.38 0.48 0.85 2.22 0.35 0.43 0.79 1.98 0.34 0.33 0.56 1.54 0.30 0.33 0.61 1.46 0.30 0.29 0.51 1.22 0.27
a G in units of radicaM00 eV, E in units of M-I cm-'. !cobs in units of M-' s-l, E in units of M-' cm-I. Assume G = 5 radicals/100 eV.
3h
r
m
r
.
2,0 r
0
.
.-
7
I + I ---> I*
0
I
I
I
1
2
3
4
Figure 5. Rate constants of iodine atom-atom reactions as a function of the inverse viscosity. The circles are for the cycloalkanes, and the squares are for the normal alkanes. The dashed line is the predicted diffusion-controlledrate constant from eq 3, and the solid line is from eq 4 with k, = 7.48 x 1OloM-I s-l and @kd = 2.02 x 1O1O/~M-' mPa. effective reaction distances for the alkyl radical-iodine scavenging reactions are given in Table 2. The reaction distances appear to decrease from about 0.8 to 0.5 nm with increasing viscosity. Iodine Atom-Atom Recombination Reactions. Iodine atoms produced by the scavenging reaction R1 will eventually recombine in reaction R2 to 12. The measured product of the G value and the extinction coefficient of the iodine atom for each of the hydrocarbons is given in Table 3. These values show a slight increase in the range 7500-9500 radicals/(100 eV M cm) with increasing carbon number. Since the iodine atom yield is equivalent to the alkyl radical yield, the extinction coefficients vary from 1500 to 1900 M-' cm-I for the hydrocarbons studied here. This observed trend may be due to the assumption of a constant G value for alkyl radical formation. The decay of the optical absorption of the iodine atom was observed to be complete at times of about 0.1-0.5 ms following the electron pulse. Analysis of the kinetics in a manner similar to that for the alkyl radical-radical reactions gave the rate constants for iodine atom-atom reactions in Table 3. There is
12640 J. Phys. Chem., Vol. 98, No. 48, 1994
almost an 7-fold decrease in the rate constant with increasing carbon number for the normal alkanes and a 4-fold decrease for the cycloalkanes. A plot of the iodine atom-atom rate constants as a function of the inverse viscosity of the medium is given in Figure 5. It can easily be seen that at the same viscosity the rate constants in the normal alkanes and cycloalkanes are similar, and all of the rate constants are greater than the diffusion-controlled rate constants predicted by eq 3. A least-squares fitting of the data to eq 4 gave the parameters ka = 7.48 x 10" M-' s-' and @'kd = 2.02 x 1O1O/~ M-' mPa. No spin or steric effects are expected for iodine atom-atom reactions in liquid hydrocarbons, and the rate constant of 2.02 x 1O'O M-' s-' at unit viscosity represents the true diffusion-controlled limit. The diffusion coefficients of iodine atoms are not known in these hydrocarbons except for hexane. In hexane, the diffusion coefficient of iodine atom has been measured to be approximately twice that of molecular and such a relationship has been assumed for all of the hydrocarbons. The resulting iodine atom diffusion coefficients and the calculated effective reaction distances for iodine atom-atom reactions are given in Table 3. The effective reaction distances decrease from about 0.5 to 0.3 nm with increasing viscosity. The small variation in the reaction distance with the various hydrocarbons is due to the fact that the diffusion coefficients of iodine atoms do not scale linearly with the inverse of the viscosity, but rather to the dependence given in eq 5. If the diffusion coefficients of iodine atoms in all of the hydrocarbons were scaled to that for cyclopentane according to the inverse viscosity, then the reaction distances would be constant at about 0.49 nm. This result implies that any iodine atom complex which is formed must be similar for all the different hydrocarbons. It is therefore unlikely that the iodine atom forms a strong charge transfer complex. It is much more likely that if any complex is formed, it is a very weak one so that it does not appreciably influence the movement and reaction of iodine atoms in the medium. This assumption would agree with the very fast diffusion controlled reaction rate constant found for iodine atom-atom reactions.
Acknowledgment. We thank Dr. S. M. Pimblott for his discussions on the parameters affecting rate constants and Dr. B. Brocklehurst for his discussions on spin relaxation of radicals. The research described herein was supported by the Office of Basic Energy Sciences of the U.S. Department of Energy. This is Contribution NDRL-3744 from the Notre Dame Radiation Laboratory. References and Notes (1) Foldiak, G.,Ed. Radiation Chemistry of Hydrocarbons; Elsevier: Amsterdam, 1981. (2) Gaumann, T.; Rappoport, S.; Ruf, A. J. Phys. Chem. 1972, 76, 3851. (3) Smaller, B.; Remko, J. R.; Avery, E. C. J. Chem Phys. 1968, 48, 5174.
(4) Rabani, J.; Pick, M.; Simic, M. J. Phys. Chem. 1974, 78, 1049.
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